What is the integral from 2/(sqrt(3)) to 2 of tarcsec(t) ?

The integral from 2/(sqrt(3)) to 2 of tarcsec(t) is (5pi-3sqrt(3))/9

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integral from 2/(sqrt(3)) to 2 of tarcsec(t)

\int_{\frac{2}{3}}^{2} t arcsec (t) d t

\frac{5 π - 3 3}{9}

Decimal

1.16797 \dots

Solution steps

\int_{\frac{2}{3}}^{2} t arcsec (t) d t

Apply Integration By Parts

: [\frac{1}{2} t^{2} arcsec (t) - \int \frac{t ^{2}}{2 t ^{2} t ^{2} - 1} d t]_{\frac{2}{3}}^{2}

= [\frac{1}{2} t^{2} arcsec (t) - \int \frac{t ^{2}}{2 t ^{2} t ^{2} - 1} d t]_{\frac{2}{3}}^{2}

\int \frac{t ^{2}}{2 t ^{2} t ^{2} - 1} d t = \frac{1}{2} t^{2} - 1

= [\frac{1}{2} t^{2} arcsec (t) - \frac{1}{2} t^{2} - 1]_{\frac{2}{3}}^{2}

Simplify

[\frac{1}{2} t^{2} arcsec (t) - \frac{1}{2} t^{2} - 1]_{\frac{2}{3}}^{2} : [\frac{1}{2} (t^{2} arcsec (t) - t^{2} - 1)]_{\frac{2}{3}}^{2}

= [\frac{1}{2} (t^{2} arcsec (t) - t^{2} - 1)]_{\frac{2}{3}}^{2}

Compute the boundaries:

\frac{5 π - 3 3}{9}

= \frac{5 π - 3 3}{9}

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What is the integral from 2/(sqrt(3)) to 2 of tarcsec(t) ?
The integral from 2/(sqrt(3)) to 2 of tarcsec(t) is (5pi-3sqrt(3))/9